Low conversion rate digital dispersion compensation

ABSTRACT

A method of suppressing effects of aliasing in a system for digitally processing a high speed signal having a symbol rate of 1/T. The high speed signal is sampled at a fractional multiple (N) of the symbol rate, wherein 1&lt;N&lt;2, to generate a corresponding sample stream, and filtered using a low-pass filter characteristic having a cut-off frequency corresponding to 1/2T. Phase distortions due to the filtering are compensated by digitally processing the sample stream.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is the first application filed in respect of the present invention.

TECHNICAL FIELD

The present invention relates to high-speed optical communicationsnetworks, and in particular to a signal equalizer in a coherent opticalreceiver.

BACKGROUND OF THE INVENTION

Optical signals received through conventional optical links aretypically distorted by significant amounts of chromatic dispersion (CD)and polarization dependent impairments such as Polarization ModeDispersion (PMD), polarization angle changes and polarization dependentloss (PDL). Chromatic dispersion (CD) on the order of 30,000 ps/nm, andpolarization rotation transients at rates of 10⁵ Hz are commonlyencountered. Various methods and systems intended to address some ofthese limitations are known in the art.

Applicant's U.S. Pat. No. 7,023,601 issued Apr. 4, 2006 and U.S. Pat.No. 7,266,306 issued Sep. 4, 2007, and Applicant's co-pending U.S.patent applications Ser. No. 10/262,944 filed Oct. 3, 2002 and Ser. No.10/307,466 filed Dec. 2, 2002 teach methods and systems forelectronically compensating chromatic dispersion and polarizationeffects in a transmitter. FIGS. 1 and 2 schematically illustraterepresentative optical transmitters capable of implementing thesemethods.

In the transmitters of FIGS. 1 and 2, the transmitter 2 receives aninput data stream x(t), and generates a corresponding output opticalsignal 4 for transmission through an optical link 6 of a communicationssystem. A receiver (not shown in FIGS. 1 and 2) at the opposite end ofthe link operates to detect the optical signal, and recover the datastream x(t).

As may be seen in FIG. 1 a, the transmitter 2 comprises a complex driver8 which receives an input data stream x(t) and outputs analog drivesignals V_(A)(t) and V_(B)(t) 10, which are supplied to respectivebranches of a complex optical modulator 12. The complex opticalmodulator 12 operates to modulate a continuous wave (CW) optical carriersignal 14 in accordance with the analog drive signals V_(A)(t) andV_(B)(t), to generate the output optical signal 4, which may be acarrier-suppressed optical signal. For simplicity of description, thedigital input signal x(t) is considered to be a serial bit stream, butan encoded symbol stream (such as Phase Shift Keying, PSK, andQuadrature Phase Shift Keying, QPSK, symbols) may also be processedusing these same techniques.

In the transmitter of FIG. 1 a, the complex driver 8 comprises a digitalfilter 16, which implements a mapping function to generate respectivemulti-bit In-phase and quadrature values I(n) and Q(n) of a desiredenvelope of the optical E-field of the optical signal 4. Preferably, themapping function also implements a compensation operator C[ ] toelectrically pre-compensate impairments of the optical link 6, such asdispersion and polarization effects. This functionality is described indetail in applicant's co-pending U.S. patent applications Ser. No.10/262,944 filed Oct. 3, 2002; Ser. No. 10/307,466 filed Dec. 2, 2002;Ser. No. 10/405,236 filed Apr. 3, 2003, and International PatentApplication No. PCT/CA03/01044 filed Jul. 11, 2003.

Various known digital filter types may be used to implement the digitalfilter 16, such as, for example, a Random Access Memory Look-up Table(RAM LUT). Alternatively, the digital filter 16 may be implemented usingFinite Impulse Response (FIR) filters, Infinite Impulse Response (IIR)filters, and Fast Fourier Transform (FFT filters). In either case, thedigital filter 16 generates the multi-bit In-phase and quadrature signalcomponent values I(n) and Q(n) at a sample rate which is about doublethe baud-rate of the input signal x(t). Thus, for example, for a baudrate of 10 Gbaud, the sample rate will be about 20 GHz.

FIG. 1 b illustrates an embodiment of the digital filter 16 known fromApplicant's co-pending U.S. patent application Ser. No. 10/262,944 filedOct. 3, 2002. In this embodiment, the input data stream x(t) is suppliedto a deserializer 18 (such as a shift register) which converts theserial data stream into an n-bit parallel input vector, which is inputto a Random Access Memory Look-Up Table (RAM LUT) 20. The RAM LUT 20 ispre-loaded with values of I(n) and Q(n) which are computed in advancefor each possible value of the input vector, based on the compensationoperator C[ ]. The width of the deserializer 18 (and thus also the inputvector and the RAM LUT 20) is determined based on the maximumanticipated dispersion of the link 6. In some embodiments, this widthmay be 64 or 128 bits. For higher speed systems, it may be desirable toextend the width beyond 128 bits, for example to 512 bits or 1024 bits,so as to enable compensation of large amounts of dispersion (e.g. 30000ps/nm or more) at line rates exceeding 10 GBaud. If desired, the RAM LUT20 may be divided into blocks (not shown) spanning a portion of thewidth of the input vector, and the respective outputs of each of theblocks combined to obtain the final values of I(n) and Q(n). With theembodiment of FIG. 1 b, obtaining a sample rate 1/T_(s) at the output ofthe RAM LUT 20 that is double the baud rate of the input data streamx(t), can be obtained by computing, for each possible value of the inputvector, a pair of I(n) and Q(n) values. A first I(n), Q(n) value iscomputed for the input vector with a phase shift of zero, while thesecond I(n), Q(n) value is computed for the input vector with a phaseshift of T/2, where T is the bit- or symbol-period of the input datastream x(t). With this arrangement, the first and second I(n), Q(n)values can be latched out of the RAM LUT 20 during each bit-period T ofthe input data stream x(t).

A non-linear compensator 22 (which may also be implemented as a RAM LUT)is used to adjust the value of each successive sample I(n) and Q(n), tocompensate non-linear performance of the transmitter 2, as described inApplicant's co-pending U.S. patent application Ser. No. 10/262,944,filed Oct. 3, 2002; and International Patent Application No.PCT/CA03/01044 filed Jul. 11, 2003. The non-linear compensator 22 may beimplemented as a separate device cascaded with the digital filter 16, asshown in FIG. 1, or may be “embedded” within the digital filter 16 byapplying the mapping function implemented by the non-linear compensator22 to the digital filter 16.

Respective high-speed Digital-to-Analog Converters (DACs) 24 a,24 b areused to convert the multi-bit sample values V_(I)(n) and V_(Q)(n) outputfrom the non-linear compensator 22 into corresponding analog signalsV_(A)(t) and V_(B)(t). If desired, the analog signals V_(A)(t) andV_(B)(t) can be conditioned, for example by means of respective filters26 a,26 b and low noise amplifiers (LNA) 28 a,28 b, in a conventionalmanner, to remove out-of-band noise and to scale the signal amplitude tothe dynamic range of the complex modulator 12.

As may be appreciated, the effects of the independent DACs 24 a,24 b,the filters 26 a,26 b and the LNAs 28 a,28 b for each signal may causedifferential propagation delays between the non-linear compensator 22and the optical modulator 12. Such differential delay can be compensatedby means of digital filters 30 a,30 b located in at least one of thesignal paths. Each digital filter 30 a,30 b can be controlled in a knownmanner to impose a selected delay, which is calculated to compensate forthe differential propagation delays experienced by each of the signalcomponents.

Referring now to FIG. 2, there is shown an embodiment of a system 32which generates a polarization multiplexed optical signal 4′, in whichrespective different data streams x_(A)(t) and x_(B)(t) are modulatedonto respective orthogonal transmitted polarizations 34 of the opticalsignal 4′. The system of FIG. 2 generally incorporates a pair ofparallel transmitters 2 of the type shown in FIGS. 1 a and 1 b. In thiscase, each transmitter 2 receives a respective input signal x_(A)(t) andx_(B)(t), which may be independent data streams or may be derived from asingle data stream. A common narrow band laser may be used for bothcomplex modulators 12, as shown in FIG. 2, although separate lasers mayalso be used if desired. In either case, both complex modulators 12operate at the same CW signal wavelength, and orthogonal polarizations.

The polarization multiplexed communications signal 4′ is generated bycombining the respective optical signals 34 a, 34 b from eachtransmitter 2, using a polarization combiner 36. Respective polarizationrotators 38 a, 38 b ensure orthogonal polarization states of the twooptical signals 34 a, 34 b. This ensures that the two optical signals 34a, 34 b are fully orthogonal, and thus can be combined into thepolarization-multiplexed communications signal 4′ without interference.

Applicant's co-pending U.S. patent applications Ser. No. 11/294,613filed Dec. 6, 2005 and entitled “Polarization Compensation In A CoherentOptical Receiver”; Ser. No. 11/366,392 filed Mar. 2, 2006 and entitled“Carrier Recovery In A Coherent Optical Receiver”; and Ser. No.11/423,822 filed Jun. 13, 2006 and entitled “Signal Acquisition In ACoherent Optical Receiver”, the content of all of which are herebyincorporated herein by reference, teach methods and systems forelectronically compensating chromatic dispersion and polarizationeffects in a receiver. FIG. 3 schematically illustrates a representativecoherent optical receiver capable of implementing these methods.

As may be seen in FIG. 3, an inbound optical signal 4″ is receivedthrough the optical link 6, split into orthogonal received polarizationsX,Y by a Polarization Beam Splitter 40, and then mixed with a LocalOscillator (LO) signal 42 by a conventional 90° optical hybrid 44. Thecomposite optical signals emerging from the optical hybrid 44 aresupplied to respective photodetectors 46, which generate correspondinganalog electrical signals. The photodetector signals are sampled byrespective Analog-to-Digital (A/D) converters 48 to yield raw multi-bitdigital signals I_(X), Q_(X) and I_(Y), Q_(Y) corresponding to In-phase(I) and Quadrature (Q) components of each of the received polarizations.

Preferably, the raw multi-bit digital signals have resolution of n=5 or6 bits which has been found to provide satisfactory performance at anacceptable cost. In the above-noted U.S. patent applications, the samplerate of the A/D converters 48 is selected to satisfy the Nyquistcriterion for the highest anticipated symbol rate of the receivedoptical signal. Thus, for example, in the case of an optical networklink 6 having a line rate of 10 GBaud, the sample rate of the A/Dconverters 48 will be approximately 20 GHz.

From the A/D converters 48, the respective n-bit signals I_(X), Q_(X)and I_(Y), Q_(Y) of each received polarization are supplied to arespective dispersion compensator 50, which operates on the raw digitalsignals to at least partially compensate chromatic dispersion of thereceived optical signal. The dispersion compensators 50 may beconfigured to operate as described in Applicant's co-pending U.S. patentapplication Ser. No. 11/550,042 filed Oct. 17, 2006.

The dispersion-compensated digital signals 52 appearing at the output ofthe dispersion compensators 14 are then supplied to a polarizationcompensator 54 which operates to compensate polarization effects, andthereby de-convolve transmitted symbols from the complex signals 52output from the dispersion compensators 50. If desired, the polarizationcompensator 54 may operate as described in Applicant's co-pending U.S.patent application Ser. No. 11/294,613 filed Dec. 6, 2005 and Ser. No.11/366,392 filed Mar. 2, 2006. The output of the polarizationcompensator 54 is a pair of multi-bit estimates X′(n) and Y′(n), 56 ofthe symbols encoded on each transmitted polarization 34 (FIG. 2). Thesymbol estimates X′(n), Y′(n) appearing at the output of thepolarization compensator 54 are then supplied to a carrier recoveryblock 58 for LO frequency control, symbol detection and data recovery,such as described in Applicant's co-pending U.S. patent application Ser.No. 11/366,392 filed Mar. 2, 2006.

In the above described system, the dispersion compensators 50 operateacross a large number of successive samples (e.g. 128 samples), whichpermits compensation of relatively severe chromatic dispersion, but at acost of a relatively slow response to changing dispersion. This slowresponse is acceptable, because of the known slow rate of change ofdispersion in real-world optical links. The polarization compensator 54,in contrast, is comparatively very narrow (e.g. on the order of about 5samples), to enable a rapid update frequency, which is necessary totrack observed high-speed polarization transients.

The above-described systems provide reliable signal acquisition,compensation of dispersion and polarization effects, carrier recoveryand data recovery even in the presence of moderate-to-severe opticalimpairments. This, in turn, enables the deployment of a coherent opticalreceiver in real-world optical networks, with highly attractive signalreach and line rate characteristics. For example, a transmitterimplementing the techniques described above with reference to FIG. 1 hasdemonstrated a signal reach of over 3000 km at a line rate of 10 GBaud,while a receiver implementing the methods described above with referenceto FIG. 3 has demonstrated equivalent performance. It is noteworthy thatthis performance has been measured with real-time continuous processing,not just burst data acquisition followed by off-line processing orsimulation. The receiver system described above with reference to FIG. 3is the only coherent optical receiver known to the applicants to haveachieved such real-time performance at multiple gigabaud.

A critical part of the design of an electronic dispersion compensationsystem, such as those described above with reference to FIGS. 1-3, isthe sampling rate of the Digital-to-Analog converter (DAC) 24 in thetransmitter and/or the Analog-to-Digital (A/D) converter 48 in thereceiver. It is standard practice to sample at an integer multiple (N)of the symbol rate. When N=1, the samples need to be aligned at thecenter of the eye in order that the signal can be accurately decoded.Because the signal bandwidth is greater than half of the sampling ratethere will be a large amount of aliasing with N=1, precluding theapplication of frequency dependent digital filtering operations such ascompensation for chromatic dispersion or Polarization Mode Dispersion(PMD).

Using the example of chromatic dispersion, the amount of phase shiftthat is caused by dispersion is proportional to the square of thefrequency, and so is the phase shift of the compensation function. Whensome energy is aliased to appear at a frequency that is not the actualoptical transmission frequency, then the wrong amount of dispersioncompensation is applied to that energy. This energy then corrupts theeye of the received signal.

When these frequency dependent filtering operations are desired it isstandard practice to sample at N≧2, so as to avoid aliasing. Thus, forexample, in the case of an optical network link having a symbol rate of10 GBaud, when N=2 the sample rate of the DAC and/or A/D converters willbe approximately 20 GHz.

More particularly, consider a system in which a baseband optical signalhaving a line (or symbol) rate of 1/T=10 Gbaud and a Besselapproximation to the ideal raised cosine spectrum (α=1.0), is sampled ata sample rate of 1/Ts=10 GHz (that is, N=Ts/T=1). This scenario, inwhich the sample period Ts=T, may be referred to as T-spaced sampling.Each sample of the sample stream is an impulse, so the frequency-domainspectrum of the sample stream will span a frequency range of 0-10 GHz,which encompasses the upper side-band of the optical signal, as may beseen in FIG. 4 a. In this drawing, the lower side-band, spanning thefrequency range between 0 and −10 GHz, is shown in dotted line. In fact,duplicates of the entire spectrum will repeat at 1/Ts=10 GHz intervalsto infinity, as shown by the dashed lines, in FIG. 4 b. As a result, thefrequency-domain spectrum of the sample stream, between 0-10 Ghz willcontain both the upper side-band of the baseband signal, and the lowerside-band of the first order harmonic. The overlap between the basebandspectrum (centered at 0) and the first order harmonics (centered at ±10GHz) represents aliasing. The use of a low-pass filter, as shown in FIG.4 c, to suppress frequencies above the base band reduces the aliasing(shaded regions of FIG. 4 b), but not enough to prevent severe signaldistortions. In this respect, it should be noted that in order to avoidsevere effects upon the eye from phase distortion, the low pass filternormally used for this operation is an analog filter having a fifthorder Bessel filter response, or an approximation to that shape. On theother hand, doubling the sample rate to 1/Ts=20 GHz (that is, T/2 orNyquist sampling) causes the duplicate spectra to repeat at 1/Ts=20 GHzintervals. As may be seen in FIG. 4 d, T/2 sampling eliminates theoverlap between the baseband and 1^(st) harmonic spectra, and thusdistortions due to aliasing.

Professor Joseph Kahn of Stanford University stated at the IEEE LEOSSummer Topical Workshop in Portland Oreg. July 2007, that N could be assmall as 3/2, and that N needed to be an integer multiple of ½ in orderfor the digital signal processing to be feasible. However, operation atN= 3/2 would require an analog low pass filter with a very steeproll-off to suppress aliasing. For the purposes of the presentdisclosure, a “steep” (or, equivalently, a “sharp”) roll-off isconsidered to be a roll-off of greater than 20 dB per decade, forexample 80 dB per decade. The desirable corner frequency is generally½T, but can vary from that value with other design considerations andcomponent tolerances. FIG. 5 a illustrates the filter characteristic ofa Chebychev filter having a suitable roll-off and a corner frequency of17.5 GHz. As may be seen in FIG. 5 b, such a filter inherently exhibitsa highly non-linear group delay characteristic, as a function offrequency. This non-linear group delay characteristic causesunacceptable phase distortions to the received eye.

With increasing demand for link band-width, it would be desirable toincrease the line rate beyond 1/T=10 Gbaud. For example, lines rates of35 GBaud and higher have been proposed. However, as the line rate isincreased, the sample rate 1/T_(s) of the digital circuits within thetransmitter and receiver must also increase, in order to maintain theT/2 sampling needed to avoid aliasing.

It will be appreciated that increased sample rates imply that the powerconsumption of the receiver must necessarily also increase, as will theheat generated by the circuits during run-time. This can impose aneffective “thermal barrier” to increasing the line rate, as highertemperatures degrade system reliability. In addition, higher samplingrates are more difficult to implement in any practical integratedcircuit (such as an Application Specific Integrated Circuit, ASIC, or aField Programmable Gate Array, FPGA) due to sampling time jitter andlimited bandwidth of the available circuit components.

Accordingly, techniques that enable reliable operation of digital signalprocessing systems at line rates above 10 Gbaud are highly desirable.

SUMMARY OF THE INVENTION

The present invention addresses the above-noted problems by providing atechnique for processing digital signals that enables the optical signalto be sampled at a sample rate less than that required to satisfy theNyquist criterion.

Thus, an aspect of the present invention provides a method ofsuppressing effects of aliasing in a system for digitally processing ahigh speed signal having a symbol rate of 1/T. The high speed signal issampled at a fractional multiple (N) of the symbol rate, wherein N<2, togenerate a corresponding sample stream, and filtered using a low-passfilter characteristic having a cut-off frequency corresponding to ½T.Phase distortions due to the filtering are compensated by digitallyprocessing the sample stream.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features and advantages of the present invention will becomeapparent from the following detailed description, taken in combinationwith the appended drawings, in which:

FIGS. 1 a and 1 b are block diagrams schematically illustratingprincipal elements and operations of a transmitter known fromApplicant's U.S. Pat. No. 7,023,601 issued Apr. 4, 2006 and U.S. Pat.No. 7,266,306 issued Sep. 4, 2007, and Applicant's co-pending U.S.patent applications Ser. No. 10/262,944 filed Oct. 3, 2002 and Ser. No.10/307,466 filed Dec. 2, 2002;

FIG. 2 is a block diagram schematically illustrating principal elementsand operations of a second transmitter known from Applicant's U.S. Pat.No. 7,023,601 issued Apr. 4, 2006 and U.S. Pat. No. 7,266,306 issuedSep. 4, 2007;

FIG. 3 is a block diagram schematically illustrating principal elementsand operations of a coherent optical receiver known from Applicant'sco-pending U.S. patent applications Ser. Nos. 11/294,613; 11/315,342;11/315,345; 11/366,392; and 11/423,822;

FIGS. 4 a-4 d illustrate aliasing in conventional digital signalprocessing systems;

FIGS. 5 a and 5 b respectively illustrate amplitude and group delaycharacteristics of a conventional Chebychev filter having a bandwidth of17.5 GHz and a steep roll-off;

FIGS. 6 a-6 c illustrate a method or reducing aliasing in accordancewith an aspect of the present invention;

FIG. 7 is a block diagram illustrating operation of a digital filterusable in the transmitter of FIG. 1, and implementing a time-domaintractional sampling technique in accordance with an aspect of thepresent invention;

FIG. 8 is a block-diagram illustrating operation of a digital filterusable in the transmitter of FIG. 1, and implementing a frequency-domainfractional sampling technique in accordance with an aspect of thepresent invention;

FIG. 9 is a block diagram illustrating operation of the re-timing blockof FIG. 8;

FIG. 10 is a block diagram schematically illustrating principal elementsand operations of a coherent optical receiver in which methods andsystems accordance with an embodiment of the present invention may beimplemented;

FIG. 11 is a block diagram schematically illustrating principal elementsand operations of the equalizer of FIG. 10;

FIG. 12 is a block diagram schematically illustrating principal elementsand operations of the retiming block of FIG. 11;

FIGS. 13 a and 13 b illustrate representative LMS loops for computingcompensation vectors for the equalizer of FIG. 11; and

FIG. 14 is a block diagram schematically illustrating principal elementsand operations of the retiming block of FIGS. 13 a and 13 b.

It will be noted that throughout the appended drawings, like featuresare identified by like reference numerals.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The present invention provides technique for transmitting digitalsignals through a high-speed optical network, in which sample ratessignificantly below T/2 can be used. Embodiments of the presentinvention are described below, by way of example only, with reference toFIGS. 6-14.

In very general terms, the present invention provides methods andsystems, in which aliasing is mitigated by oversampling the receivedoptical signal, at a fractional multiple N of the symbol rate, whereinN<2, which corresponds to a sample period T_(s) of T_(s)>T/2. Fractionalsampling avoids the thermal barrier associated with the extreme samplerates implied by full T/2 sampling, and yet shifts the 1^(st) harmonicspectra away from the baseband signal. This shifting of the 1^(st)harmonic spectra reduces overlap at the tails. High order analog lowpass filtering of the optical signal (either in the optical orelectrical domain) with a very steep roll-off and a cut-off frequencycorresponding to ½T can be implemented in the receiver to suppress thealiasing terms. The otherwise crippling phase distortions generated bythis analog filtering can be characterized mathematically, and so can becompensated digitally.

For example, consider a 35 GBaud optical signal generated with a“squared” spectrum (i.e. raised cosine, α=0.1), which exhibits a sharproll-off at 17.5 GHz and suppressed signal energy beyond thesefrequencies, as illustrated in FIG. 6 a. Transmitters of the type knownfrom Applicant's U.S. Pat. No. 7,023,601 issued Apr. 4, 2006 and U.S.Pat. No. 7,266,306 issued Sep. 4, 2007, for example, are readily capableof generating an optical signal having the desired squared spectrum.Oversampling the optical signal at the receiver using 7T/8 sampling(that is, N=Ts/T=8/7) corresponds to a sample rate of 1/T_(s)=8/7×35GHz=40 GHz, so that the 1^(st) harmonic spectra will be centered at 40GHz. As may be seen in FIG. 6 c, this creates a margin of about 5 GHzwidth between the baseband and 1^(st) harmonic spectra, whichsignificantly reduces the overlap between these spectra. Low-passfiltering in the receiver, for example using a conventional Chebychev orButterworth-8 filter characteristic with a sharp roll-off and a cut-offfrequency of ½T=17.5 GHz, as shown n FIG. 6 b effectively suppressesenergy of the 1^(st) harmonic between 20 and 40 GHz. The residualaliasing terms, shown by the shaded region of FIG. 6 c, are low enoughthat the resulting errored bits can be successfully corrected byconventional Forward Error Correction (FEC) processing techniques.

The description below presents, by way of example only, threealternative embodiments in which link impairments are compensated atfractional sample rates, in accordance with the present invention, asfollows: a time-domain implementation in the transmitter; afrequency-domain implementation in the transmitter, and afrequency-domain implementation in the receiver.

Transmitter: Time Domain

As discussed above with reference to FIGS. 1 a and 1 b, the digitalfilter 16 described in Applicant's co-pending U.S. patent applicationsSer. Nos. 10/262,944 and 10/307,466 compensates link impairments (inaccordance with the compensation operator C[ ]), and generates I(n) andQ(n) sample streams at a sample rate of double the baud rate of theinput data stream x(t). Since both of these operations are performed inthe time domain, it will be seen that the transmitters of FIGS. 1 and 2implement time-domain compensation with T/2-sampling. In the presentembodiment, this performance is extended to provide time-domaincompensation with fractional sampling.

FIG. 7 conceptually illustrates operation of a digital filter 60 usablein the transmitter of FIGS. 1 and 2, in place of the digital filter 16,to provide time-domain impairment compensation with 8T/9-sampling (i.e.N=9/8). Thus for example, if the input data stream x(t) has a baud rateof 35 GBaud, the sample rate of the I(n),Q(n) sample streams output fromthe digital filter will be 39.38 GHz. The remaining elements of thetransmitter of FIGS. 1 and 2 can remain largely unchanged, except as maybe necessary to accommodate the different sample rate.

In the embodiment of FIG. 7, the digital filter 60 comprises a set ofnine parallel filter blocks 62, each of which comprises a deserializer18 and RAM LUT 20 as described above with reference to FIG. 1 b. Eachfilter block 62 receives the input data stream x(t) with the delaysindicated below in table 1, and outputs a respective I(n),Q(n) sample ina period of 8T. The respective RAM LUT 20 of each filter is loaded withvalues of I(n) and Q(n) computed for each possible value of the inputvector, at the phase shift indicated below in table 1 and shown in FIG.7.

Filter Block Delay Phase Shift 0 0 +4T/9 1  T +3T/9 2 2T +2T/9 3 3T +T/9 4 4T 0 5 5T  −T/9 6 6T −2T/9 7 7T −3T/9 8 7T +5T/9

In operation, during each clock cycle (of period 8T), 8 bits of theinput data stream x(t) are latched into the respective deserializer 18of each filter block 62, with the appropriate delays. The resultinginput vectors are then applied to each RAM LUT 20, to yield nineI(n),Q(n) sample values, which can then be interleaved (at 64) in thecorrect order and latched out of the digital filter 60. The combinedeffect of the delays imposed on the input data stream x(t) and the phaseshifts applied during calculation of the I(n),Q(n) values loaded intoeach RAM LUT 20, is the generation of nine, T/N=8T/9-spaced I(n),Q(n)sample values during each clock cycle, which is the desired result.

The approach described above with reference to FIG. 7 is valid becausethe actual desired envelope of the optical E-field of the output opticalsignal 4 is a continuous analog function. Each successive input vectorsupplied to the RAM LUT 20 is an impulse which, via the compensationoperator C[ ], maps to an instantaneous value the desired opticalE-field. However, for any given input vector, the contour of the E-fieldenvelope can be fully defined from the compensation operator C[ ]. Sincethe analog contour of the E-Field envelope is known, it is possible tocompute instantaneous values of the desired E-field at any desired phaserelative the input vector, to obtain the values of I(n) and Q(n) whichneed to be loaded into the respective RAM LUT 20 of each filter block62. It may be appreciated that, at extreme phase shift values theaccuracy of the computed instantaneous optical E-field envelope valuewill become increasingly inaccurate, due to the finite length of theinput vector. However, for the very small phase shifts described above,the accuracy of this calculation is sufficient.

It will be appreciated that the above approach can be suitably modifiedto obtain other values of N. In a more generic sense, N can be definedas N=n/d, in which case the above approach can be described byimplementing the digital filter 60 comprising a set of n parallel filterblocks 62. During each clock cycle (of period dxT), a set of d symbolsof the input data signal is latched into each filter block 62 with theappropriate delay, and the corresponding values of I(n) and Q(n) fromeach filter block 62 interleaved.

Similarly, it will be appreciated that other values of the phase shiftscan applied during calculation of the I(n),Q(n) values loaded into eachRAM LUT 20. The important characteristic is that the phase shifts anddelays are cooperatively selected to ensure that, for each clock cycle(of period dxT) the n values of I(n) and Q(n) output by each filterblock 62 represent instantaneous values of the desired optical E-fieldthat are evenly spaced in time.

The filters 26 can be configured as reconstruction filters having alow-pass filter characteristic (such as, for example, a Butterworth-8filter) having a sharp roll-off at about ±½T=17.5 GHz to suppressaliasing terms beyond about 20 GHz, as described above with reference toFIG. 6. The phase distortions introduced by these filters 28 can becharacterised as a function of frequency, using well known techniques.This information can then be used to modify the compensation operator C[] so as to compensate the phase distortions introduced by the filters28.

As noted above, FIG. 7 shows a conceptual illustration of a digitalfilter 60 implementing the Time-Domain technique. As may be appreciated,a practical digital filter could be implemented which follows thisconceptual model fairly closely. However, it is anticipated that thoseof ordinary skill in the art will, in the light of the present teaching,be able to design various alternative implementations.

Transmitter: Frequency Domain

The Time-domain techniques described above with reference to FIG. 7 areparticularly suited to transmitters in which the input data stream x(t)is a serial bit stream. While the digital filter 60 of FIG. 7 can bemodified to accommodated a stream of encoded symbols (e.g. PSK or QPSKsymbols), or nonlinearly equalized signals, such modifications tend togreatly increase complexity and cost of the circuitry. In most cases,frequency domain techniques offer a more efficient approach.

FIG. 8 is a block diagram illustrating operation of a digital filter 66usable in the transmitter of FIGS. 1 and 2, in place of the digitalfilter 16, to provide frequency-domain impairment compensation with7T/8-sampling (i.e. N=8/7).

In the embodiment of FIG. 8, the input data signal x(t) is supplied toan encoder 68, which outputs a corresponding multi-bit complex valuedsymbol stream. For example the input data signal x(t) may take the formof one or more serial bit-streams, and the multi-bit complex valuedsymbol stream output from the encoder 68 are PSK or QPSK symbols. Otherencoding techniques may be used as desired, for example OpticalOrthogonal Frequency Division Multiplexing (O-OFDM). In any case, theT-spaced multi-bit symbols output from the encoder are deserialized (at70) and the resulting m-word input vector {a+jb} latched into a fastFourier Transform (FFT) block 72. The FFT block is a conventionalcomplex FFT block having a width selected to compensate the maximumanticipated chromatic dispersion of the optical link. In someembodiments, the FFT block 72 may have a width of 896 taps taps, inwhich case m=448.

The array {R} output by the FFT block 72 is then supplied to a retimingblock 74, which operates to re-time the array {R} from the T-spacedtiming of the encoder 68 to the desired 7T/8 sampling of the DACs 24.

By way of example only, consider an embodiment in which a 35 GBaudsymbol stream from the encoder 68 is to be processed and transmittedthrough the optical link 6. In order to avoid aliasing, it is desired toover-sample the symbol stream at a fractional sampling frequency of8/7T, which corresponds with a sample rate of 1/T_(s)=40 GHz. In thiscase, the array {R} output by the FFT block 72 spans a frequency rangeof 0-35 GHz. The lower half of this array (corresponding to a frequencyrange of 0-17.5 GHz) encompasses the upper side-band of the basebandspectrum of the encoded input signal, while the upper half of the array(corresponding to 17.5-35 GHz) encompasses the lower side band of the1^(st) harmonic spectrum. In the case of an FFT block of 896 taps width,7T/8 sampling can be accomplished by increasing the width of thespectrum to 1024 taps. The values of the added 128 taps can bedetermined by exploiting the fact that the upper and lower side bandsare nominally mirror images of each other, so that the tap values aresubstantially symmetrical about the center of the array.

Following this example, the retiming block 74 can be constructed asshown in FIG. 9. Thus, the FFT taps (0-511) are supplied to taps 0-511of the re-timed array; and FFT taps (384-895) are supplied to taps512-1023 of the re-timed array. This results in a retimed spectrum 1024taps in width, as desired.

Returning to FIG. 8, the re-timed array {R′} is then supplied to aFrequency Domain multiplier 76, which applies a compensation vector {C}to yield a modified array {M}. The compensation vector {C} can becomputed using a transform of a 1^(st) order dispersive function to atleast partially compensate chromatic dispersion of the optical link 6.The phase distortions introduced by the analog filters 28 can also becharacterised as a function of frequency, using well known techniques.This information can then be used to modify the compensation vector {C}so as to compensate phase distortions introduced by the analog filters26.

The modified array {M} output from the Frequency Domain multiplier 76 isthen supplied to an Inverse Fast Fourier Transform (IFFT) block 78,which operates at the 7T/8-sampling rate of 40 GHz to generate timedomain data 80, in the form of a complex valued vector having a widthequal to the IFFT 78, which, in the illustrated embodiment is N=1024taps. The IFFT output data 80 is divided into two blocks {v⁰}, and {v¹},of which {v¹ _(X)} is delayed by one clock cycle (at 82) and added to{v⁰ _(X)} (at 84) to yield the digital filter output in the form of acomplex valued vector {I(n)+jQ(n)} representing p=512T/N=7T/8-spacedI(n),Q(n) values of the desired optical E-field envelope.

Receiver: Frequency Domain

FIG. 10 illustrates principle elements of a coherent optical receiverwhich utilizes fractional sampling in accordance with the presentinvention. The embodiment of FIG. 10 implements the required sample rateconversion in the frequency domain. In principle, sampling rateconversion can be performed accurately in the time domain within thereceiver. However, this option is not described in detail herein becausethe complexity of the circuit implementation makes this alternative lessdesirable than the frequency-domain embodiment described below.

As may be seen in FIG. 10, the coherent optical receiver generallycomprises a Polarization Beam Splitter 40; 90° optical hybrid 44;photodetectors 46; and A/D converters 48. All of these elements mayoperate as described above with reference to FIG. 3, except that in thiscase, the A/D converters 48 are driven to sample the photodetectorcurrent at a sample rate T_(s) of T>T_(s)>T/2. For example, in someembodiments, the sample rate Ts may correspond to T_(s)=7T/8. In anoptical communications system in which the line rate is 1/T=35 GBaud,7T/8-sampling corresponds with a sample rate of 40 GHz. Analoganti-aliasing filters 86 inserted between the photodetectors 46 and A/Dconverters 48 implement a conventional low-pass filter characteristic(such as, for example, and Butterworth-8 filter) having a sharp roll-offat about 1/2T=17.5 GHz to suppress aliasing terms beyond about 20 GHz,as described above with reference to FIG. 6. The phase distortionsproduced by these anti-aliasing filters 86 can be digitally compensatedas described below. The raw digital sample streams I_(X), Q_(X), andI_(Y), Q_(Y) generated by the A/D converters 48 are supplied to a signalequalizer 88. If desired, timing control methods described inApplicant's co-pending U.S. patent application Ser. No. 11/550,042 filedOct. 17, 2006, including the use of elastic stores (not shown in FIG.10) between the A/D converters 48 and the equalizer 88 may be used toensure at least coarse phase alignment between samples at the equalizerinput.

In general, the equalizer 88 operates to compensate chromatic dispersionand polarization rotation impairments, as well as the phase distortionsproduced by the analog filters 86. The compensated signals 56 outputfrom the equalizer 88 represent multi-bit estimates X′(n) and Y′(n) ofthe symbols encoded on each transmitted polarization 34 of the receivedoptical signal 4. The T-spaced (that is, at the timing of transmittedsymbols) symbol estimates 56 X′(n), Y′(n), are supplied to a carrierrecovery (CR) block 58 for LO frequency control, symbol detection anddata recovery, such as described in Applicant's co-pending U.S. patentapplication Ser. No. 11/366,392 filed Mar. 2, 2006. FIG. 11 is a blockdiagram illustrating principle elements of a representative equalizer 88useable in the receiver of FIG. 10.

In the embodiment of FIG. 11, the raw digital sample streams I_(X),Q_(X), and I_(Y), Q_(Y) generated by the A/D converters 48 aredeserialized (at 90) to form m-word input vectors {r^(I)x+jr^(Q)x} and{r^(I)y+jr^(Q)y} which span one half the width of the FFT. During eachclock cycle, the m-word vectors {r^(I)x+jr^(Q)x} and {r^(I)y+jr^(Q)y}are latched into the respective X- and Y-polarization FFT blocks 92,along with the corresponding “old” vectors (at 91) from the previousclock cycle. Each FFT block 92 is a conventional complex FFT blockhaving a width selected to enable compensation of the maximumanticipated chromatic dispersion of the received optical signal. In someembodiments, each FFT block 92 may have a width of 1024 taps, in whichcase m=512. The arrays {R^(A)X} and {R^(A)Y} output by the FFT blocks 92are then supplied to a Frequency Domain Processor (FDP) 94.

In the embodiment of FIG. 11, the FDP 94 comprises a respectivetranspose-and-add functional block 96 for each polarization, and across-compensation block 98. The transpose-and-add block 96 may operatein generally the same manner as described in Applicant's co-pending U.S.patent application Ser. No. 11/550,042 filed Oct. 17, 2006. Thus, theX-polarization transpose-and-add block 96x operates to add the FFToutput array {R^(A)X} to a transposed (conjugate) version of itself { R_(X) ^(A)}, with respective different compensation vectors {C⁰ _(X)} and{C^(T) _(X)} to yield intermediate array {T^(A) _(X)}. Compensationvectors {C⁰ _(X)} and {C^(T) _(X)} can be computed using a transform ofa 1^(st) order dispersive function to at least partially compensatechromatic dispersion of the optical link; and/or using empiricalknowledge of propagation delays encountered in each signal path betweenthe optical fiber 6 and the equalizer input to compensate residualsample phase errors in the raw digital signals generated by the A/Dconverters 48. In either case, the phase distortions introduced by theanalog filters 86 can also be characterised as a function of frequency,using well known techniques. This information can then be used to modifythe compensation vectors {C⁰ _(X)} and {C^(T) _(X)} so as to compensatephase distortions introduced by the analog filters 86. Of course, theY-polarization transpose-and-add block 96 _(Y) will operate in anexactly analogous manner.

The cross-compensation block 98 applies X-polarization vectors H_(XX),H_(XY) to the X-polarization intermediate array {T^(A)X}, andY-polarization vectors H_(YY), H_(YX) to the Y-polarization intermediatearray {T^(A) _(Y)}. The multiplication results are then added togetherto generate modified vectors {V^(A) _(X)} and {V^(A) _(Y)}, as may beseen in FIG. 11. The X- and Y-polarization vectors H_(XX), H_(XY),H_(YY) and H_(YX) are preferably computed using a transform of the totaldistortion at the output of the equalizer 88, as will be described ingreater detail below. At a minimum, the X- and Y-polarization vectorsH_(XX), H_(XY), H_(YY) and H_(YX) impose a phase rotation whichcompensates polarization impairments of the optical signal, and sode-convolve the transmitted symbols from the raw digital sample streamsI_(X), Q_(X), and I_(Y), Q_(Y) generated by the A/D converters 48. Thoseof ordinary skill in the art will recognise that the illustratedcross-compensation block 98 implements an inverse-Jones matrix transferfunction, which compensates the polarization effects. In thisformulation, the vectors H_(XX), H_(XY), H_(YY) and H_(YX) are providedas the coefficients of the inverse-Jones matrix. The width of theinverse-Jones matrix is equal to that of the intermediate arrays {T^(A)_(X)} and {T^(A) _(Y)}, and so is based on the expected maximumdispersion of the received optical signal to be compensated by theequalizer 88.

The modified arrays {V^(A) _(X)} and {V^(A) _(Y)} output by the FDP 94are then supplied to respective retiming blocks 100, which operate tore-time the modified arrays {V^(A) _(X)} and {V^(A) _(Y)} from the 7T/8sample timing of the A/D converters 48 to the desired T-spaced timing ofthe multi-bit symbol estimates 56.

By way of example only, consider an embodiment in which a 35 GBaudoptical signal is sampled at a sample rate of 1/T_(s)=40 GHz. The A/Dconverters 48, FFT blocks 92, and FDP 88 will all operate at the samplerate of 1/T_(s)=40 GHz. In this case, each of the arrays {R^(A) _(X)}and {R^(A) _(Y)} output by the FFT blocks 92, and thus each of themodified arrays {V^(A) _(X)} and {V^(A) _(Y)} output by the FDP 94 spana frequency range of 0-40 GHz, with upper side band (USB) spectrum at0-20 GHz and lower side band (LSB) at 20-40 GHz, respectively. Inprinciple, retiming of the modified arrays {V^(A) _(X)} and {V^(A) _(Y)}can be accomplished by extracting the center portion of each array, andthen supplying the remaining portions to the IFFT blocks 102.

In an embodiment in which each FFT block 92 has a width of 1024 taps(that is taps n=0 . . . 1023), with USB at n=0-511 and LSB atn=512-1023. Retiming the modified arrays {V^(A) _(X)} and {V^(A) _(Y)}can be accomplished by recognising that, within each array, the combinedspectrum is nominally symmetrical about the center of the array.Consequently, the upper and lower halves of the array can be overlappedby a selected number of taps in the center portion of the array, and thethus “overlapped taps” added together. The number of overlapped taps isselected so that, after the addition operation, the total number ofremaining taps corresponds with the desired width of the retimed array.In the above example, the 1024 taps of the FFT output spans a frequencyrange of 0-40 GHz, and it is desired to reduce the frequency range to0-35 GHz. This corresponds with a reduction of 128 taps. Thus, the upperand lower halves of each modified array {V^(A) _(X)} and {V^(A) _(Y)}are overlapped by 128 taps and the overlapped taps added together. Thisresults in the 128 taps lying above the center of the array (taps n=512. . . 639) being added to the 128 taps lying below the center of thearray (taps n=384 . . . 511), and the summation result supplied to taps384-511 of the retimed array, as shown in FIG. 12. The taps lying aboveand below this center region (at taps 0-383 and 640-1023, respectively)are then supplied to corresponding upper and lower portions of theretimed array, again as shown in FIG. 12. This operation effectivelyremoves 128 taps from the center of each of the modified arrays {V^(A)_(X)} and {V^(A) _(Y)} to yield retimed arrays {V^(A) _(X)}′ and {V^(A)_(Y)}′, in the form of complex multi-bit vectors having a width of 896taps, and spanning a frequency range of 0-35 GHz.

The retimed arrays {V^(A) _(X)}′ and {V^(A) _(Y)}′ are then supplied tothe IFFT blocks 102, which operate at the T-spaced symbol rate of 35 GHzto generate time domain data 104, in the form of a complex valued vectorhaving a width equal to the IFFT 102, which, in the illustratedembodiment is N=896 taps. The IFFT output data 104 is divided into twoblocks {v⁰ _(X)}, and {v¹ _(X)}, of which {v¹ _(X)} is selected as theequalizer output 56 in the form of a complex valued vector {v^(I)_(X)+jv^(Q) _(X)} representing p=448T-spaced complex valued estimatesX′(n) and Y′(n) of the transmitted symbols. The other IFFT output block,{v⁰ _(X)}, is discarded.

Preferably, the X- and Y-polarization vectors H_(XX), H_(XY), H_(YY) andH_(YX) are computed at sufficient speed to enable tracking, and thuscompensation, of high-speed polarization rotation transients. This maybe accomplished using the Least Mean Squares (LMS) update loop 110illustrated in FIG. 11, and described in greater detail below withreference to FIGS. 12 and 13.

FIG. 13 a shows an LMS update loop, according to one embodiment of theinvention, for calculating polarization vectors H_(XX) and H_(YX). Adirectly analogous LMS loop for calculating the polarization vectorsH_(XY) and H_(YY) is shown in FIG. 13 b. In the embodiment of FIGS. 13 aand 13 b, the carrier recovery block 58 (FIG. 11) operates as describedin Applicant's co-pending U.S. patent application Ser. No. 11/366,392filed, Mar. 2, 2006. Thus, the carrier recovery block 58 is divided intotwo parallel processing paths 112 (only the X-polarization path 112 x isshown in FIG. 13 a, and the Y-polarization path 112 y is shown in FIG.13 b), each of which includes a decision circuit 114 and a carrierrecovery loop comprising a carrier phase detector 116 and a phaserotator 118. In general, the phase rotators 118 use a carrier phaseestimate generated by the respective carrier phase detector 116 tocompute and apply a phase rotation (correction) k(n) to the symbolestimates X′(n) and Y′(n) received from the signal equalizer 88. Thedecision circuits 114 use the phase-rotated symbol estimatesX′(n)e^(−jK) ^(X) ^((n)) and Y′(n)e^(−jK) ^(Y) ^((n)) to generaterecovered symbol values X(n) and Y(n), and the phase detectors 116operate to detect respective phase errors Δφ between the rotated symbolestimates X′(n)e^(−jK) ^(X) ^((n)) and Y′(n)e^(−jK) ^(Y) ^((n)) and thecorresponding recovered symbol values X(n) and Y(n).

Referring to FIG. 13 a, the H_(XX) LMS update loop receives the phaseerror correction k_(X)(n) of each successive symbol estimate X′(n),which is calculated by the phase detector 116 as described inApplicant's co-pending U.S. patent application Ser. No. 11/366,392. Inaddition, the rotated symbol estimate X′(n)e^(−jK) ^(X) ^((n)) and itscorresponding decision value X(n) are also received from the carrierrecovery block 58, and compared (at 120) to obtain a complex symbolerror value e_(X), which is indicative of residual distortion of thesymbol estimate X′(n). In some embodiments it is desirable to format theoptical signal into data bursts comprising a plurality of data symbolsseparated by a SYNC burst having a known symbol sequence. In such cases,a selector 122 can be used to supply a selected one of the decisionvalues X(n) and the known SYNC symbols to the comparator 120. With thisarrangement, the selector 122 can be controlled to supply the known SYNCsymbol sequence to the comparator 120 during each SYNC burst, so thatthe error value e_(X) is computed using the known SYNC symbols ratherthan the (possibly erroneous) decision values X(n).

In order to minimize calculation complexity through the LMS update loop,the resolution of the complex symbol error e_(X) is preferably lowerthan that of the symbol estimate X′(n). For example, in an embodiment inwhich the symbol estimate X′(n) has a resolution of 7 bits for each ofthe real and imaginary parts (denoted herein as “7+7 bits”), the complexsymbol error e_(X) may have a resolution of, for example, 3+3 bits. Itwill be noted, however, that the present invention is not limited tothese resolution values.

The phase rotation k_(X)(n) is combined with the corresponding recoveredsymbol value X(n), for example using a Look-up-Table (LUT) 124, togenerate a corresponding complex value X(n)e^(jk) ^(X) ^((n)) with adesired resolution (e.g. 3+3 bits) matching that of the symbol errore_(X). This allows the phase error X(n)e^(jk) ^(X) ^((n)) and symbolerror e_(X) to be multiplied together (at 126) to obtain a complex valued_(X) indicative of the total residual distortion of the symbol estimateX′(n).

Applicant's U.S. patent application Ser. No. 11/423,822 filed Jun. 13,2006 describes methods and systems for signal acquisition in a coherentoptical receiver. As described in U.S. patent application Ser. No.11/423,822, during a start-up operation of the receiver (or duringrecovery from a “loss-of frame” condition), LO frequency control, clockrecovery, dispersion compensation and polarization compensation loopsimplement various methods to acquire signal, and stabilize tosteady-state operation. During this “acquisitions period”, the rotatedsymbol estimates X′(n)e^(−jK(n)) and their corresponding decision valuesX(n) are probably erroneous. Accordingly, in the embodiment illustratedin FIGS. 13 a and 13 b, a window select line 128 may be used to zero outthose values of the distortion vector d_(X) which are computed fromnon-synch symbols. Values of the distortion (d_(X)) which are computedfrom the known SYNC symbols are likely to be valid, even during signalacquisition, and thus are left unchanged.

The symbol distortion values d_(X) are deserialized (at 129) to generatea p-word (following the above example, p=448) distortion vector {d^(I)_(X)+jd^(Q) _(X)}, which is padded with a p-word zero vector (i.e. avector comprising p zeros) 131 and is input to a Fast Fourier Transform(FFT) block 130, which calculates the frequency domain spectrum of thesymbol distortion vector {d^(I) _(X)+jd^(Q) _(X)}. As will beappreciated, values of the distortion vector {d^(I) _(X)+jd^(Q) _(X)}are generated at the symbol timing. In the case of 7T/8 sampling, thisis less than the sample rate of the raw digital sample streams I_(X),Q_(X), and I_(Y), Q_(Y) generated by the A/D converters 48, and it istherefore necessary to adjust the timing of the error values d_(X) tomatch the sample timing. At the same time, the width of the frequencydomain spectrum of the (re-timed) symbol distortion vector d_(X) shouldpreferably correspond with that of the intermediate array {T^(A) _(X)}.With this arrangement, each value of the intermediate array {T^(A) _(X)}can be truncated (at 132) to match the resolution of the FFT blockoutput (e.g. 3+3 bits), and then a conjugate of the truncated arraymultiplied with the FFT output array (at 134), to compute alow-resolution correlation between {T^(A) _(X)} and the retimed FFToutput. This correlation vector can then be scaled (at 136) to obtain anupdate vector {u_(xx)}, which is accumulated (at 138) to obtain a vectorrepresentation of the total distortion of the intermediate array {T^(A)_(X)}. Truncating the total distortion vector, for example by taking the7+7 most significant bits, yields the cross-compensation vector H_(XX).

As noted above, directly analogous methods can be used to compute eachof the other cross-compensation vectors H_(XY), H_(YY) and H_(YX), whichare therefore not described herein in detail.

As may be seen in FIGS. 13 a and 14, re-timing of the symbol distortionvector {d^(I) _(X)+jd^(Q) _(X)} can be accomplished by inserting are-timing block 140 at the output of the FFT 130. In this case, thewidth of the FFT 130 is selected to match the width of the IFFT blocks102 of the equalizer 88 (e.g. N=896 taps, following the above example).With this arrangement, the retiming block 140 can be constructed asshown in FIG. 14. Thus, the FFT taps (0-511) are supplied to taps 0-511of the re-timed spectrum, while FFT taps 384-895 are supplied to taps512-1023 of the re-timed spectrum. This results in a retimed spectrum of1024 taps in width, which corresponds with the intermediate arrays{T^(A) _(X)}, as desired.

In the embodiments described above, the reconstruction (anti-aliasing)filters are provided by analog electrical filters. However, otherfiltering methods, including optical band pass filtering and digitalfiltering techniques can be used either in conjunction with or insteadof the analog electrical low pass filters. Analog filtering can be donein any or all of the transmitter, optical link, and receiver.

For simplicity of description, a single carrier is used in the describedmethods. Multiple optical or electrical carriers that are coherent,partially coherent or incoherent can be used. Various other signalformats and digital compensation methods can be used, such as OpticalOrthogonal Frequency Division Multiplexing, or subcarrier multiplexing.

In the foregoing embodiments, 7T/8 and 8T/9 sampling is described. Theseratios are convenient for the retiming techniques described, but otherratios may equally be used. Furthermore, while simple fractional ratios(i.e. wherein both the numerator and the denominator are integers) areoften convenient, this is not essential. Non-integer ratios may be used,if desired.

In the foregoing embodiments, values of 1<N<2 (e.g. N=8/7 and N=9/8) areused. Values of N in this range are useful for the retiming techniquesdescribed. However, with suitable programming, values of N equal to orless than 1 may also be used.

The embodiments of the invention described above are intended to beillustrative only. The scope of the invention is therefore intended tobe limited solely by the scope of the appended claims.

1. A method of suppressing effects of aliasing in a system for digitallyprocessing a high speed signal having a symbol rate of 1/T, the methodcomprising: filtering the high speed signal using a low-pass filtercharacteristic having a cut-off frequency corresponding to approximately½T, and a roll-off greater than 20 dB per decade; sampling the highspeed signal at a fractional multiple (N) of the symbol rate, whereinN<2, to generate a corresponding sample stream; and digitally processingthe sample stream to compensate phase distortions due to the filtering.2. The method as claimed in claim 1, wherein N<3/2.
 3. The method asclaimed in claim 1, wherein N>1.
 4. The method as claimed in claim 1,wherein the high speed signal is an input data stream x(t) to betransmitted through a link of an optical communications system, andwherein sampling the high speed signal comprises generating a stream ofmulti-bit samples of a desired complex optical E-field envelope of anoptical signal for conveying the high speed signal through the link,based on the input data stream x(t).
 5. The method as claimed in claim4, wherein the fractional multiple N=n/d, and wherein generating thestream of multi-bit samples comprises, during each clock cycle of perioddxT: converting the high speed signal into a set of n parallel inputvectors, each input vector having a respective predetermined delay; foreach input vector, computing a respective multi-bit sample value of thedesired complex optical E-field envelope at a predetermined phase shiftrelative the input vector; and interleaving the computed multi-bitsample values.
 6. The method as claimed in claim 5, wherein computingthe respective multi-bit sample value of the desired complex opticalE-field envelope comprises applying a compensation operator C[] to theinput vector, the compensation operator C[] being computed to compensateat least chromatic dispersion of the link.
 7. The method as claimed inclaim 6, wherein digitally processing the sample stream to compensatephase distortions due to the filtering comprises: characterizing thephase distortions as a function of frequency; and computing thecompensation operator C[] using the phase distortion characteristic soas to compensate the phase distortions.
 8. The method as claimed inclaim 5, wherein the predetermined delay of each input vector and thepredetermined phase shift used for computation of the respectivemulti-bit sample value for each input vector, are cooperatively selectedsuch that the n multi-bit sample values computed during each clock cyclerepresent successive instantaneous values of the desired complex opticalE-field envelope that are evenly spaced in time.
 9. The method asclaimed in claim 8, wherein at least the step of computing, for eachinput vector, the respective multi-bit sample value is performed by aset of n parallel filter blocks, and wherein, for values of n=9 and d=8,the predetermined delay of each input vector and the predetermined phaseshift used for computation of the respective multi-bit sample value foreach input vector are: Filter Block Delay Phase Shift 0 0 +4T/9 1  T+3T/9 2 2T +2T/9 3 3T  +T/9 4 4T 0 5 5T  −T/9 6 6T −2T/9 7 7T −3T/9 8 7T+5T/9


10. The method as claimed in claim 4, wherein generating the stream ofmulti-bit samples comprises: computing a Fast Fourier Transform (FFT) ofthe input data stream x(t) to generate an array {R} representing afrequency domain spectrum of the input data stream x(t); processing thearray {R} to generate a retimed array {R′} having a width correspondingto N times the width of the array {R}; and computing an Inverse FastFourier Transform (IFFT) of the modified array {M}.
 11. The method asclaimed in claim 10, wherein computing the Fast Fourier Transform (FFT)of the input data stream x(t) comprises steps of: encoding the inputdata stream x(t) using a selected encoding scheme to generate acorresponding multi-bit complex valued symbol stream; and computing aFast Fourier Transform (FFT) of the multi-bit complex valued symbolstream.
 12. The method as claimed in claim 11, wherein the encodingscheme is selected from the set consisting of: Phase Shift Keying (PSK);Quadrature Phase Shift Keying (QPSK); and Optical Orthogonal FrequencyDomain Multiplexing (O-OFDM).
 13. The method as claimed in claim 10,wherein processing the array {R} to generate a retimed array {R′}comprises increasing the width of the array {R} by a factor of N. 14.The method as claimed in claim 13, wherein increasing the width of thearray {R} comprises: supplying a lowermost set of taps of the array {R}to a corresponding set of lowermost taps of the retimed array {R′}; andsupplying an uppermost set of taps of the array {R} to a correspondingset of uppermost taps of the retimed array {R′}; wherein the lowermostset of taps of the array {R} at least partially overlaps the uppermostset of taps of the array {R}, and wherein the set of lowermost taps ofthe retimed array {R′} is contiguous with the set of uppermost taps ofthe retimed array {R′}.
 15. The method as claimed in claim 10, whereindigitally processing the sample stream to compensate phase distortionsdue to the filtering comprises: characterizing the phase distortions asa function of frequency; and computing the compensation vector using thephase distortion characteristic so as to compensate the phasedistortions.
 16. The method as claimed in claim 1, wherein the highspeed signal is modulated on at least one transmitted polarization of anoptical signal received through an optical link of an opticalcommunications system, and wherein sampling the high speed signalcomprises: generating respective in-phase and quadrature multi-bit rawdigital sample streams for each received polarisation of the opticalsignal, a sample rate of the multi-bit raw digital sample streams beingN times the symbol rate of the high speed signal; processing themulti-bit raw sample streams to compensate at least chromatic dispersionand polarization effects of the optical link; and retiming theprocessing result to the symbol rate of the high speed signal.
 17. Themethod as claimed in claim 16, wherein processing the multi-bit rawsample streams and retiming the processed sample stream comprises:computing a Fast Fourier Transform (FET) of the at least two multi-bitraw digital sample streams to generate at least two arrays {R}, eacharray {R} representing a frequency domain spectrum of a respectivereceived polarization of the received optical signal, and digitallyprocessing the arrays {R} to generate at least one modified array {V},each modified array {V} representing a frequency-domain spectrum of acorresponding transmitted polarization of the optical signal.
 18. Themethod as claimed in claim 17, wherein retiming the processing resultcomprises changing a width of each modified array {V} by a factor of1/N.
 19. The method as claimed in claim 18, wherein changing a width ofeach modified array {V} comprises: defining contiguous upper and lowersets of taps of the modified array {V}, each set of taps encompassinghalf of the taps of the modified array {V}; overlapping the upper andlower sets of taps by a predetermined number of taps in a center portionof the modified array {V}; adding the overlapped taps together, andsupplying the addition result to corresponding central taps of a retimedarray {V}′; supplying uppermost taps lying above the center region ofthe modified array {V} to corresponding uppermost taps of the retimedarray {V}′; and supplying lowermost taps lying below the center regionof the modified array {V} to corresponding lowermost taps of the retimedarray {V}′.